One of the simplest factor copulas is a Gaussian static factor copula, which [1]} suggest
for a single factor, and [2]} consider for a larger number of factors. The multiple factor
copula can be defined as follows.
Let \(\widetilde{\mathbf {Z}} \sim N_m(\mathbf {0},\Lambda \Lambda ^\top +D)\) , where \(\Lambda =\lbrace \lambda _{j,k}\rbrace \)  is an \(m\times p\)  matrix of factor loadings, \(D=\mbox{diag}(d_1,\ldots ,d_m)\)  is a diagonal matrix of idiosyncratic
variations,
and typically \(p<<m\) .
The implicit copula of \(\widetilde{\mathbf {Z}}\)  is a Gaussian copula, as outlined
in Section REF . To derive the parameter matrix \(\Omega \) , set the diagonal matrix
\(S=\mbox{diag}(\Lambda \Lambda ^\top +D)=\mbox{diag}\left(\sum _{k=1}^p \lambda _{1,k}^2+d_1,\ldots ,\sum _{k=1}^p \lambda _{m,k}^2+d_m\right)\,,\) 
